Outline. Drawing the Graph. 1 Homework Review. 2 Introduction. 3 Histograms. 4 Histograms on the TI Assignment

Transcription

1 Lecture 14 Section on Hampden-Sydney College Fri, Sep 18, 2009

2 Outline 1 on on 5 6 Even-numbered

3 on Exercise 4.25, p The following is a list of homework scores for two students: Student A: 80, 52, 86, 94, 76, 48, 92, 69, 79, 45. Student B: 73, 87, 81, 75, 78, 82, 84, 74, 80, 76. (a) Construct a back-to-back stem-and-leaf plot of the data. (b) Which student do you think has done better work? Explain your answer.

4 on Solution (a) The back-to-back stem-and-leaf display: Student A Student B

5 Solution (b) I think Student B did better work. Even though he didn t get any A s, his work was consistent acceptable. on

6 on We will learn a third method of displaying quantitative data, the histogram. This method takes more effort than the other two, but it is more flexible and produces a much better display. And, it can be done on.

7 on We will learn a third method of displaying quantitative data, the histogram. This method takes more effort than the other two, but it is more flexible and produces a much better display. And, it can be done on.

8 on We will learn a third method of displaying quantitative data, the histogram. This method takes more effort than the other two, but it is more flexible and produces a much better display. And, it can be done on.

9 on Definition () A class is an interval of values. Typically, it includes the lower endpoint and does not include the upper endpoint. Definition (Histogram) A histogram is a graphical display of quantitative data in which the data are distributed among classes and each class is represented by a rectangle. The size of the rectangle is proportional to the number of observations in the class.

10 vs. Bar Graphs on Bar graphs are for qualitative data are for quantitative data. We indicate this difference by leaving a gap between the bars of a bar graph and no gap between the rectangles of a histogram.

11 Example on Draw a histogram of the rainfall data, in centimeters

12 Drawing on Find the maximum value, the minimum value, and the range. Minimum = Maximum = Range = Max Min = =

13 Drawing on Divide the data into classes of equal width. The classes must not overlap. Choose a convenient starting point. Choose a convenient class width. Write the endpoints of each class.

14 Drawing on Let s let the class width be 5 (other choices are possible). Then the number of classes will be at least or = 7.432,

15 Drawing on Or we could begin by deciding to use 8 classes (other choices are possible). Then the width must be at least or = 4.645,

16 Drawing on Let s let the starting point be 0. : 0.00 up to 4.99 (but not including 5.00) 5.00 up to up to up to up to up to up to up to 39.99

17 Drawing on We may write the classes in either of two ways. Interval notation: [low, high). [0.00, 5.00), [5.00, 10.00), [10.00, 15.00), etc. [ and ] mean include endpoints. ( and ) mean exclude endpoints.

18 Drawing on Range notation: low - high , , , etc. With this notation, the endpoints are assumed to be included. Therefore, be sure the endpoints do not overlap. Yet be sure that no possible values are left out.

19 Drawing Count the number of observations in each class. This is the frequency of the class. on

20 Drawing on Draw horizontal and vertical axes. On the horizontal axis, show the class limits. On the vertical axis, show uniform reference points representing frequencies or percentages that are appropriate for the data, starting at 0. Over each class, draw a rectangle whose height is the frequency, or relative frequency, of that class.

21 Drawing on Frequency Class

22 Drawing on Frequency Class

23 Drawing We could have used 7 classes of width 6, starting at 0. on

24 Drawing on Frequency Class

25 Drawing Or we could have used 10 classes of width 4, starting at 0. on

26 Drawing on Frequency Class

27 Drawing on Guidelines: Never use too few or too many classes. Usually 5 to 12 classes is about right. Use simple round numbers for the class boundaries. Mark off the vertical axis uniformly, showing regular reference points, not the actual frequencies. The vertical scale must start at 0.

28 TI-83 - on TI-83 Histogram Enter the data into list L 1. {2.82,24.18,0.20,...,0.74} L 1 Press STAT PLOT Select Plot1. Press ENTER. Turn Plot1 on. Select histogram type. Specify list L 1.

29 TI-83 - on TI-83 Histogram Press WINDOW Set Xmin to the starting point. Set Xmax to the last endpoint. Set Xscl to the class width. Set Ymin to 0 (or 1 for a margin). Set Ymax to the maximum frequency. Press GRAPH. The histogram appears.

30 TI-83 - on TI-83 Histogram Or, press ZOOM. Select ZoomStat (#9). The histogram appears.

31 TI-83 - Frequency Distributions on TI-83 Histogram After getting the histogram, press TRACE. The display shows the first class and its frequency. Use the left arrow to see the other class frequencies.

32 on Read Section 4.4.4, pages Let s Do It! 4.14, Page 259, exercises 30, 31, 33-36, 38. Chapter 4 review, p. 284, exercises 58, 59,

33 Even-numbered on Page 259, 30, 34, 36, (a) Qualitative. (b) A pie chart or a bar graph Poor Fair Good Very Good Excellent 4.34 (a) About 20%. (b) Yes. It is skewed to the left.

34 Even-numbered on Page 259, 30, 34, 36, (a) 15 (b) (c) Symmetric, unimodal. (d) Symmetric, bimodal. (e) (i) Two-sided. 4 (ii) 20. (iii) Accept H 0.

35 Even-numbered Page 259, 30, 34, 36, (a) on

36 Even-numbered on Page 284, 58, (a) 4.68 (a)